Comparing Acceleration Of Xander, Finley, And Max A Physics Problem

In this article, we delve into a fascinating physics problem involving three individuals – Xander, Finley, and Max – and their respective velocities and time taken to achieve those velocities. Understanding acceleration is crucial in physics, as it describes the rate at which an object's velocity changes over time. By analyzing the data provided, we can determine who accelerated the most and least, offering valuable insights into their motion. We will explore the concepts of initial velocity, final velocity, time, and acceleration, and apply the relevant formulas to calculate each person's acceleration. This analysis will provide a clear understanding of how each individual's velocity changed over the given time intervals and allow us to rank them based on their acceleration.

The Scenario: Velocity and Time

Let's first recap the scenario. Xander achieved a final velocity of 4.5 meters per second (m/s) in 3.5 seconds. Finley reached a final velocity of 3.6 m/s in 4.2 seconds. Max, on the other hand, reached a final velocity of 7.3 m/s in just 1.2 seconds. Crucially, all three started from rest, meaning their initial velocity was 0 m/s. This starting condition simplifies our calculations, as we only need to consider the final velocity and the time taken to reach it. The differences in their final velocities and the times they took to reach those velocities are the key pieces of information we need to compare their accelerations. Calculating acceleration involves determining how quickly each person's velocity changed, and this comparison will reveal who had the highest and lowest acceleration.

Calculating Acceleration: The Formula

To determine who accelerated the most and least, we need to calculate their individual accelerations. Acceleration is defined as the rate of change of velocity per unit time. The formula for calculating acceleration is:

Acceleration (a) = (Final Velocity (vf) - Initial Velocity (vi)) / Time (t)

Since all three individuals started from rest, their initial velocity (vi) is 0 m/s. This simplifies the formula to:

a = vf / t

Now, let's apply this formula to each person's data. For Xander, the final velocity (vf) is 4.5 m/s, and the time (t) is 3.5 seconds. For Finley, the final velocity (vf) is 3.6 m/s, and the time (t) is 4.2 seconds. And for Max, the final velocity (vf) is 7.3 m/s, and the time (t) is 1.2 seconds. By plugging these values into the formula, we can calculate the acceleration for each person and then compare their results. Understanding the acceleration formula is fundamental to solving this problem, as it directly relates the change in velocity to the time taken for that change.

Xander's Acceleration

Let's calculate Xander's acceleration using the formula: a = vf / t. Xander's final velocity (vf) is 4.5 m/s, and the time (t) he took to reach this velocity is 3.5 seconds. Plugging these values into the formula, we get:

a = 4.5 m/s / 3.5 s

a ≈ 1.29 m/s²

Therefore, Xander's acceleration is approximately 1.29 meters per second squared (m/s²). This value represents the rate at which Xander's velocity increased over the 3.5 seconds. Calculating Xander's acceleration is the first step in our comparative analysis, providing a baseline against which we can compare the accelerations of Finley and Max. The units of acceleration, m/s², indicate that the velocity is changing by 1.29 meters per second every second.

Finley's Acceleration

Next, we'll calculate Finley's acceleration using the same formula: a = vf / t. Finley's final velocity (vf) is 3.6 m/s, and the time (t) he took to reach this velocity is 4.2 seconds. Plugging these values into the formula, we get:

a = 3.6 m/s / 4.2 s

a ≈ 0.86 m/s²

Thus, Finley's acceleration is approximately 0.86 m/s². This value indicates that Finley's velocity increased at a slower rate compared to Xander. Determining Finley's acceleration is crucial for comparing his motion to that of Xander and Max. A lower acceleration value suggests that Finley's velocity changed less rapidly over the 4.2 seconds.

Max's Acceleration

Now, let's calculate Max's acceleration. Using the formula a = vf / t, Max's final velocity (vf) is 7.3 m/s, and the time (t) he took to reach this velocity is 1.2 seconds. Plugging these values into the formula, we get:

a = 7.3 m/s / 1.2 s

a ≈ 6.08 m/s²

Therefore, Max's acceleration is approximately 6.08 m/s². This is significantly higher than both Xander's and Finley's accelerations. Max's high acceleration indicates a rapid increase in velocity over a short period, making him the fastest to accelerate among the three. This calculation highlights the importance of considering both final velocity and the time taken to reach that velocity when determining acceleration.

Comparing Accelerations: Who Accelerated the Most and Least?

Now that we have calculated the accelerations of Xander, Finley, and Max, we can compare them to determine who accelerated the most and who accelerated the least. Let's recap the results:

• Xander's acceleration: approximately 1.29 m/s²
• Finley's acceleration: approximately 0.86 m/s²
• Max's acceleration: approximately 6.08 m/s²

By comparing these values, it is clear that Max had the highest acceleration at 6.08 m/s². This means Max's velocity increased the fastest over the given time period. On the other hand, Finley had the lowest acceleration at 0.86 m/s², indicating the slowest rate of change in velocity. Xander's acceleration of 1.29 m/s² falls in between Max and Finley, showing a moderate rate of change in velocity.

Conclusion: Ranking the Accelerations

In conclusion, by calculating and comparing the accelerations of Xander, Finley, and Max, we have determined their relative rates of change in velocity. Max had the highest acceleration, meaning he reached his final velocity in the shortest amount of time. Finley had the lowest acceleration, indicating a slower increase in velocity. Xander's acceleration was in between Max and Finley. Therefore, we can rank them in terms of acceleration from highest to lowest as follows:

1. Max
2. Xander
3. Finley

This analysis demonstrates the application of fundamental physics principles to understand and compare motion. Understanding acceleration is crucial in many real-world scenarios, from vehicle performance to sports activities. By applying the formula a = vf / t, we can quantitatively assess how quickly an object's velocity changes and make meaningful comparisons.

This detailed analysis highlights the importance of understanding the relationship between velocity, time, and acceleration. The differences in their accelerations showcase how varying these factors can impact motion. Through this exploration, we've gained a deeper appreciation for the principles of physics and their application in everyday scenarios.